Three numbers form an AP, if the first and third are 5&245 respectively, find the two possible values
d is the difference between consecutive values in an AP
... there is only one value here
... 5 + d = 245 - d
r is the ratio between consecutive values in a GP
... there would be two possible values
... 5 r = 245 / r
u didnt explain it very well all the way thanks alot
Tracy -- we might take you seriously if you had made your complaint in standard English.
You didn't explain it very well. Thanks a lot.
What Scott did makes perfect sense to me.
Perhaps you will understand it better if we use the standard definitions.
term(1) = a = 5
term(3) = a+2d = 245
so:
5 + 2d = 245
2d = 240
d = 120
So the 3 terms are 5, 125, and 245
There is only one answer, not two like you stated.
If you wanted the 3 terms to be a GP, then follow Scott's steps to get the two possible answers.
To find the two possible values of the second number in the arithmetic progression (AP), we need to find the common difference (d) of the AP first. Once we have the common difference, we can determine the second number by adding the common difference to the first number.
In this case, the first number (a₁) is 5 and the third number (a₃) is 245. Let's use the formula for the nth term of an AP:
aₙ = a₁ + (n - 1) * d
We can plug in the known values into the formula to create two equations:
For a₃: 245 = 5 + (3 - 1) * d
Simplifying, we get: 245 = 5 + 2d
For a₁: 5 = 245 - (n - 1) * d
Simplifying, we get: 5 = 245 - 2d
Now, we can solve these two equations simultaneously to find the common difference (d):
245 = 5 + 2d
-2d = 245 - 5
-2d = 240
d = -240 / -2
d = 120
Now that we have found the common difference (d = 120), we can find the second number (a₂) by adding the common difference to the first number:
a₂ = a₁ + d
a₂ = 5 + 120
a₂ = 125
Thus, the two possible values for the second number in the arithmetic progression are 125 and 125.